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The Stepping Stone Method

The Stepping Stone Method Once an initial feasible solution to a transportation problem is determined by any of the previous methods, the next step is to solve the model for the optimal solution. The Stepping Stone Method is an iterative technique used to evaluate the cost effectiveness of  the shipping routes not currently in the solution. When applying it, we test each unused cell, or square, in the transportation table by asking : What would happen to the total shipping cost if one unit of product was tentatively shipped to an unused route? To illustrate the same, let us look at the initial solution of the Bengal Plumbing Problem derived by the Northwest Corner Rule. Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A 100 Rs. 5 0 Rs. 4 0 Rs. 3 0 100 Plant B 200 Rs. 8 0 100 Rs. 4 0 Rs. 3 0 300 Plant C Rs. 9 0 100 Rs. 7 0 200 Rs. 5 0 300 Ware...
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The Intuitive Lowest Cost Method

The Intuitive Lowest Cost Method Or The Minimum Cell Cost Method The Intuitive Lowest Cost Method is a cost based approach to finding an initial solution to a transportation problem. It makes allocations starting with the lowest shipping costs and moving in ascending order to satisfy the demands and supplies of all sources and destinations. This straightforward approach uses the following steps. Identify the cell with the lowest cost. Allocate as many units as possible to that cell without exceeding the supply or demand. Then cross out the row or column or both that is exhausted by the above assignment. Move on to the next lowest cost cell and allocate the remaining units. Repeat the above steps as long as all the demands and supplies are not satisfied.  When we use the Intuitive Approach to the Bengal Plumbing problem, we obtain the solution as below. Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F War...
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Vogel's Approximation Method (VAM)

The Vogel's Approximation Method In addition to the North West Corner and Intuitive Lowest Cost Methods for setting an initial solution to transportation problems, we can use another important technique - Vogel's Approximation Method (VAM). Though VAM is not quite as simple as Northwest Corner approach, but it facilitates a very good initial solution, one that is often the optimal solution. Vogel's Approximation Method tackles the problem of finding a good initial solution by taking into account the costs associated with each alternative route, which is something that Northwest Corner Rule did not do. To apply VAM, we must first compute for each row and column the penalty faced if the second best route is selected instead of the least cost route . To illustrate the same, we will look at the Bengal Plumbing transportation problem. Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A...
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